Compound angle measuring device



Sept. 27, 1949. PALMER 2,483,228

COMPOUND ANGLE MEASURiNG DEVICE v Filed Oct. 25, 1945 3 Sheets-Sheet 1 INVENTOR. LAWRENCE F. PALMER.

Sept. 27, 1 949. F. PALMER 2,483,228

CQMPOUND ANGLE MEASURING DEVICE I Filed Oct. 23, 1945 :5 Sheets-Sheet 2 1N VEN TOR. F. PALM ER Sept. 27,1949.

s Sheets-Sheet 3 I 2e- 24 I \\\\\//11 INVENTOR.

" 6 LAWRENCE F. PALMER.

F. PALMER 4 2,483,228

Patented Sept. 27 1949 COMPOUND ANGLE MEASURING DEVICE Lawrence F. Palmer, Mentor, Ohio, assignor-to Alfred B. Bower, Toledo, Ohio, as trustee Application October 23, 1945, Serial No. 623,971

3 Claims. (01. 33-1) This invention relates to'calculators and particularly to a measuring device designed to be used in the solution of compound angle problems.

Compound angle problems arise, for example, where one is dealing with solid geometric figures bounded by intersecting planes. There are numerous angles which can be measured upon such a solid and persons dealing with them are often confronted with a situation wherein some .of the angles are known and other angles must: be deduced from them. In each surface there are what may be called surface angles between the lines of intersection of adjacent planes, and between each intersecting pair of planes is what may becalled the dihedral angle of the pair, meaning by this the angle between their intersections with an imaginary plane which is normal to their common line. 7

.Machinists andtool makers in particular are frequently faced with situations of this kind wherein a work-piece has surfaces at odd angles and must be so placed upon the work holder of a .shaper, planer, grinder, or the like that the surface to be machined will be parallel to the plane of the pathof travel of the tool. Such set-ups while not diflicult to one well versed in trigonometry and geometry are at least intricate and time consuming, and, to one not well versed in these subjects, can be most difficult and even quite baflling.

Apart from the question of difliculty is that of the likelihood of error resulting from the use of tables, as is necessary when dealing with the trigonometric functions. The trigonometric tables are reliably accurate but the danger of misapplying them or copying from them incorrectly is always present.

For the above reasons there has always been felt a great need for a calculating instrument on which the desired results could be read directly.

The general object of the present invention is to provide a device on which the known quantities in a compound angle problem may be set up and from which the desired answers may be read off directly.

' Another object is to provide such a device which will be in as compacta form as possible and simple in construction and in use.

Referring now to the drawings, Fig. 1 is a perspective view of one embodiment of the compound angle measuring device of my invention; Fig. 2 is a diagrammatic representation of the principal planes of the device; Fig. 3 is a side elevation; Fig. 4 is a fragmentary perspective view of the Side opposite that in Fig. 1; Fig. 5 is a transverse section taken on the line 5-5 in Fig. 3; Fig. 6 is a fragmentary section taken on the line 6-6 of Fig. 5; Fig. '7 is an orthographic projectional showing of a work-piece, the set-up of which may be calculated with my device; Fig. 8 is a perspective view of the work-holding fixture of a machine tool, such asa shaper, with the work-piece of Fig. 7 set up thereon; and Fig. 9 is a similar View of the work holder of a grinder.

As shown in the drawings, my device comprises a number of circular scales so pivoted and slidable on each other that the parts may be put in adjustable angular relationship with each other. The basic scheme of the device is shown in Fig. 2 where it will be seen that the various parts, and the angular relationship therebetween, may be represented by four planes of adjustable relative positions. The primed numbers on the planes are the same as the numbers unprimed of the corresponding parts of the device. The primed letters of the various angles are the same as the unprimed letters denoting the scales on the device where such angles are read. Two planes l0 and H are normal to a third plane l2-I3' and at an adjustable dihedral angle A with each other. A fourth plane l4l5' may be put in any desired angular relationship with the other planes. Its line of intersection with the plane I0 is at an angle S with the base, and its line of intersection with the plane H is at an angle T with the base. The surface angle B between the two lines of intersection of the plane I l-I5 is measured in that plane and, finally, the dihedral angle between the plane M I5 with the plane I0 is measured at X, and that with the plane II is measured at Y. Any three of these angles are sufiicient to determine the plane and its position relative to the other planes. 'The remaining three angles definitely follow from the configuration and their values may be read on the scales of the device.

Referring now to the drawings of the device itself, it will be seen that the base l2 has an annular ring l3 rotatably slidable thereon. The base is provided with a rabbet at I 6 to receive the ring and with cleats l1 to keep it in place. One of the cleats is provided with a thumb screw l8 and may therefore clamp. the ring in an adjusted position. The base I2 is also provided with a scale A and the ring I3 carries a zero mark I!) and a cooperating Vernierv scale. Thus, by means of the scale A, the angular position of the ring relative to the base may be determined.

The vertical plane ID of the diagram is defined by the semi-circular member l carried by a block 28] secured to the base it The adjustable plane I4|5 of the diagram is defined in the instrument by two rings l4 and [5. The ring I4 is carried at two diametrically opposite points on pivot pins 2| in the ends of the semi-circular member ID. The line of intersection of the plane of the rings and the semicircular member is' thus definedzby the axis of the pivot pins, and the angle of this line with the horizontal can be adjusted by rotating the semicircular member circumferentially on the block as will later be described. The anguiarjposi tion of the line may be determined by means of a scale S on the member m and ai-coactin-gzero' mark 22 appropriately placed orrthe supportifl. The member In is provided with-adovetailed: rib 23 which is slidable in a similarly shaped groove in the support 20. Means are provided,as"best seen in Fig. 6, for clamping the member 10 in its adjusted position. As there shown, a vertically slidable zpin 2-4'is adaptedgto press against the dovetailedrib. thumb screw 25'i's provided-with al -conical end which -coacts= with -aconical indentation ZS-in: thepin 24. The wedgin'g action.

obtained when the=thumb screw is turned inwardly raisesthe pin against the dovetail and effectively clamps it. Thearcuate support by the block ifl and the interfitting parts of the rib a'Iid' groove 1 rigidly 'maintain the: member to in a verticaLplane.

Thedihedralangle X not the diagram. is measuredby mean-slot a scaleiX 'on'ancarc 2-1 rigidly carried by the ring" M. ThetarcZ-T is semi-circulai fand its :e'nds are rsecurely'abolted or otherwise rigidly secured; toidian'i etricaliy.oppositepoints '28 on the ring l ti These pointsfare at90 around the ring. Mirom the pivots-2 tzarid "thus, since the plane of the-arms! ispernranently at right angleswithathe ring, itris norma'l to the aX-ismf the pivots. Therefore, the scale-:X: and a cooperating zeroemarkzfi carriedibyithe member Incorrectly gives the measure: of. the= dihedra1= angle between theiring and th'e member-1 0a- Thezero mark 2-9, with -itsassociated lvemier"scale, is conveniently carried by? an" angle .pieceiiilltbolted-to the member I10 as at "H in Fig; 4. .Als'o bolted 'to the member H1 is .a.-;c1amp comprising a bracket and athumbsc'rew; whereby the are 71 may be main tained:iniadjustedlpcsitiom The vertical-plane til inthe diagram is defined inzthe .=instrument by th'e annular trackw'ay' FL This is rigidlyfmai'ritai'ried' in a vertical-plane by the supporting blocks 32 to whichit is bolted andwhich are: in. turn bolted .to' the ring 1-3 I on the base. the dihe'di'al' angle*betweenthe pian'e ofithe member lifl 'and'that of the trackway H" mayibeladjus'tedby'means ofthe slippingring I 3 on tlre based- 2 and measured by the'scale'A.

T'lIhe line (it interse'ctiomofthepl'ane ll andof the plane ofiti re tiltablering is obtainedby means of a traveler orslide33 whih runs in a groove 31' iniithe member M The slide 33has sufficient circumferential 'support in the trackway H to" maintain-it in theplanexof the latter. A second rin'g t-E is 'slidablewithin the ringl tandi is supported therebyby means ofan-appropriate tongue and annular groove joint; for "example; ;At-"diametrically opposite points of thering' l5-- pivotal connectionaasat 3'6, are made with depending ears on tne slide'fi. Thus-the axis of thepivots" 36' defines the intersection line of-the planes of the-ringanifthe trackway ll. Thean'gle between this line o'f intersection and the" horizontal plane' is -measured by' the scaleT onthe 'trackway 'l I 4 and the zero mark 31 and Vernier scale on the slide 33.

As the ring I5 is adjustably rotated within the ring 14, the angle between the axis of the pivots 36 and that of the pivots 2| is measured by means of a scale B on the ring [4 and a zero mark 44 on the ring l5. The angle so measured is that at B in the diagram.

To measure the dihedrali angle between the plane of the ring'and trackwavas indicated at Y in the diagram, the scale Y and zero mark 38 are provided. The scale Y is inscribed on an are 39 the-endszof whichware rigidly attached to the ring 45, at points 40, to maintain it in a plane norrna l to-'tl'iato'fthe ring. The points 40 are at fi alongthering from the pivots 36. The arc39- is slidable ima notch 4| in the slide 33 and the zero mark 38 is carried on an arcuate block flsecured to the slide 33 by means of an angle piece 43. By this construction the scale Y at: all timesflmeasures the .d-ihedrall zangle in a plane whichii's at the same-time normal' to the plane of the ringsaa-nd to that of the slide 33 and trackway l I.

It will be un'd'erstood tliat the" instrument is'so constructed? that;thetpartsvareali in strict: align-- ment. That is, the'fourpivot:pinsi at' flfiiandl zl all lie'iinithe same plane atheaxes ofi tne track way I I and ofithe semicircuiaifi member: Minter sect at thesamepoint; asthe ax e's of the pairs of pivots 'and the asri'sbi rotation oi the baseiring' I3 is coincident vi ith the lime e1 intersection ot the planes oiti'ie-memitens Wand it! and com tains 'the common-point or intersection of the other axes.

Referring now to Figs-'1,8 anii 9gtheoperation of the instrumentwili beshown 'as applied tp a practical problems iHere the' rect'angul'ar work piece of Fig. '7 is to be-formed w-ithamangular match the -si'cl'es= of whih-ame to 'be at the" designated angles with the sides oi the work-piece As shown in 'Fig; 8; i t' is desired lto -so orient' the block fi-orrth'e workl'iolder -of-a shaperthat the surface 46 will lie'in -a horizontal plane as defined by the pathsdii movementof thecuttingtoot-anti feed of themachine wa that the line of inter section Y -52" will be parallel with-the line of movement of the cuttingtool as defined by'the line Y YL Threeangles-must-beknown to' properi'yprient thewvorkpiece, namely, 'F aud t The angle G is immediately known by i'nspectibm as 1 the pIa-neof the tilting tabfe =41 is =the=- same as that of" the plan view" in Fih. '7; showing that v the workpiece 1 must" be twisted z thereon.

Referrin -how to "my device, will be found that one has a choiceofia'number of wayspf setting"-upthproblem. This'is" often the case but I have found it best to $0 chjoosethe planes that'- they wiil be found in their normal positibns on theinstrument. In thepresent-case;:there= fore; it is best to represent-the plane of'the' tiltin'g table-by meansof the tilting "ring EA -T5.

Horizontal planes 'in" the" set-up m'ay' berepresented by the horizontal plane or the" base 'of' the instrument and two appropriate vertical planes may be found in the set-up to correspond to the vertical planesof 1:0 and Hi Onesuch plans is conveniently taken -.transverse to the cutting motion orthesfraper; that is, theplane of the scale '4"I11DOII which theang'leE is to be set. The second verticaliplane is conveniently taken as thatlof the surface "49' of the Work-pieceas it is in "this'plane that-the angle of.2l given betweenithe' horizontal surface 548 andithe 'til'ting'table': It Will b'e' noted thatthe' surface 49 is atruly vertical plane because,- as :seen in Fig. .,:the front elevational .view shows it to be normal .to the machinedsurface 46. Transferring the known quantities now to the instrument, we choosethe plane of. H]. as that ofgthe surface 49 and set. upon the :scale S the angleof 21. Since the surface 49rises normal tothe tilting. table, we place the member In normal to the plane; of thering l4il5 by settingthe scale Xlat 90. .Referring again to Fig. 8, we see that the line of the hinges of the tilting table defines-the sneer intersection of the plane of. the table withfla transverse vertical pl'aneof the machine which, in the instrument,

is represented by the member H. 'We also see that the surface 49 of thework-piece meets the tiltingtable in a line whose angle with the line of the hinges is thecomplement of the angle G ,The angle G has previously been found to be 32 and therefore the angle betweenrthevertical planes as measured in the plane of the tilting table is 58. On the instrument, the angle inthe plane of the rings l4--l5 is given by the scale B. Therefore, we now, rotate the ring I 3 upon the base 12 until the axes of the two pairs of pivots in the rings I4-.-.l5 are at an angle of Three known quantities having been set on the instrument, definitely establishing the relationship of the parts, the desired results can be read directly on the instrument scales. The angle E of Fig. 8, which is a measure of the amount by which the line of hinges of the tilting table must be shifted from the horizontal, may be read on the scale T. In this case 57'. The angle Fin Fig. 8 is seen to be the complement of the dihedral angle between the tilting table and the vertical transverse plane. This angle is given by the scale Y in the instrument since this scale measures the dihedral angle between the rings M-l5 and the member H, in this case 71 58'. Angle F is the complement of this, or 18 2'. Thus all that is needed to be known for the setting up of the work-piece has now been determined in a simple and accurate manner.

Another example of the application of my instrument may be demonstrated in connection with Fig. 9 wherein the same work-piece is to be set up on the work holder of a machine such as a grinder. The surface 46 is again to be horizontal and the line of intersection Y'-Y' is to be arallel to the path of the grinding wheel as defined by the line Y-Y. The work-piece 45 is mounted on a wedge block or tilting table '5!) which, in turn, is mounted on a rotatable table 5! adjustable in a horizontal plane. Two angles must be determined in this case, namely, the angle K of the wedge block and the angle J of the rotating table. As before, the surface 49 is in a vertical plane and hence the angle K is seen by inspection to be 21.

Referring now to the instrument, the base is taken as a horizontal plane and the rings l4-l5 are taken. as the surface of the wedge. The two vertical planes which are of interest comprise the one defined by the surface 49 and any one which is parallel to the path of the tool, that is. with the line Y'Y' or Y-Y. The member 9 is taken as the vertical plane of surface 49 and the angle of 21 is set up on the scale S thereon. Since the face of the wedge block is normal to the surface 49, the rings l4-l5 are placed normal to the member In by setting the scale X at 90. As shown in the plan view of Figs-7, the angle. between the vertical planes as measured in the surface of the.wedge is 32,v

and so. thering .I3 is. now rotated on the base l2, directly corresponding to rotation of the horizontal table 5| in Fig. 9, until the ring 15 has revolved inside the ring l4 through 32 as measured on the scale B. The. angle through which the base ring l3 has been rotated is now read on the scale A, giving the desired results for the While I have illustrated'a particular embodi ment of my invention, I do not wish to be limited to any of the'details here shown as it will be ap-' parent that numerous modifications could be made by one familiar with the principles of myinvention and substantially the same results would' be obtained. I claim: 1.' An angle calculator having a stationary horizontal base comprisingtwo relatively rotationally settable sections, an arcuate support on one of the base sections, an arcuate member circum-- ferentially slidable in a vertical plane in the arcuate support, a tiltable member comprising two relatively rotationally settable sections one of which is pivoted at diametrically opposite points on the arcuate member, a second arcuate member rigidly carried by the second section of the base and defining a vertical plane, a traveler slidable on the second arcuate member and having pivotal connections at two diametrically opposite points on the second section of the tiltable member whereby the axis of pivotal connections is constrained to lie in the vertical plane of the second arcuate member, means for measuring the angle made with the base by the axes of the two pairs of pivots respectively, means for measuring the angle of rotation of the tiltable member about the first-named pair of pivots with respect to the first arcuate member, and means for measuring the angle of rotation of the tiltable member about the second-named pair of pivots with respect to the second arcuate member.

2. An angle calculator having a horizontal base comprising two relatively rotationally settable sections, an arcuate support on one of the base sections, an arcuate member circumferentlally slidable in a vertical plane in the arcuate support, a tiltable member comprising two relatively rotationally settable sections one of which is pivoted at diametrically opposite points on the arcuate member, a second arcuate member rigidly carried by the second section of the base and defining a vertical plane, a traveler slidable on the second arcuate member and having pivotal connections at two diametrically opposite points on the second section of the tiltable member whereby the axis of pivotal connection is constrained to lie in the vertical plane of the second arcuate member, a circular scale rigidly supported on the first section of the tiltable member in a plane normal to the axis of the first pair of pivots and an indicator carried by the first arcuate member for coaction therewith, and a second circular scale rigidly supported on the second section of the tiltable member in a plane normal to the axis of the second pair of pivots and an indicator carried by the traveler for coaction with 76 the second scale. 

